The present invention relates to an automatic generation system of a program for a numerical calculation for a physical model represented by a partial differential equation, and more particularly to a method for generating a program suitable for a boundary-fitted method for analyzing an arbitrary shape.
Since the program for the numerical calculation carries out mapping transformation by equations (generally partial differential equations) representing physical laws which govern a shape of a simulation domain and physical phenomena, in accordance with conditions at a boundary of the domain, it is highly troublesome to generate it by a program. Accordingly, it is desirable to automatically generate the program in accordance with simple input data.
Several such programs have been proposed, for example, by Morris, S. M. et al "SALEM-A Programming System for the Simulation of Systems Described by Partial Differential Equation", Proc. Fall Joint Computer Conf., Vol. 33, pages 353-358 (1968); Cardenas. A. F. et al "A language for partial Differential Equations", Comm. ACM, vol. 13, No. 3, ,pp 184-191 (1970.3); Rice, J. R. et al "ELLPACK progress and plans, in Elliptic Problem Solvers", pp 135-162, Academic Press (1981); IMSL Inc., "TWODEPEP : A finite Element Program"3rd ed (1982).
Since the above methods have limitations on the form of the partial differential equation, a program language called Differential Equation Solver and a program for generating a numerical simulation program by using such a program language have been proposed. For example, Umetani et al "A numerical Simulation Language for vector/parallel processors" (Ford et al : Problem Solving Environments for Scientific Computing Elsevier Science publishers B.V. (Holland) 1987, pp 147-162), describes a method for generating a program for numerical calculation for a partial differential equation to be simulated in accordance with a finite differential method. A method for generating a program in accordance with the finite differential method is also disclosed in Japanese
Patent Application No. 61-54762 entitled "Automatic Apparatus for Numerical Calculation Procedure". It relates to a method for determining a DO loop when a FORTRAN numerical calculation program is automatically generated by the finite differential method.
A physical phenomenon is determined if a partial differential equation which governs an unknown physical quantity, a spatial domain which is a domain of the partial differential equation and a boundary condition or initial condition thereof are given. The numerical calculation for simulating the physical phenomenon on a computer can be performed by the finite differential method or a numerical analysis called a boundary-fitted method by defining the partial differential equation, the boundary condition, the spatial domain, mapping of the spatial domain, and discretization (to approximate physical quantities at mesh points governed by the partial differential equation) of differential operators contained in the partial differential equation, boundary condition and initial condition.
In the numerical simulation which uses a general purpose computer, it is impossible to realize the function only with the above information. Thus, a mechanism for automatically generating a program for controlling the general purpose computer in accordance with the above designation is provided so that the numerical simulation can be controlled with as less designation as possible.